Markov solution processes: Modeling human problem solving with procedural knowledge space theory

Algorithms for the adaptive assessment of procedural knowledge and skills

“…As such, they cannot be empirically validated, for instance, by means of standard goodness-of-fit statistics. A probabilistic model that incorporates all the critical deterministic assumptions of PKST has been recently developed by Stefanutti et al, ( 2021 ). It is based on the notion of a Markov solution process (MSP), a stochastic process that represents the problem solution behavior of a problem solver.…”

“…In the sequel, every single problem state in the ToL problem space is uniquely referred to by using a pair ab of numbers, where a stands for one of the six spatial arrangements whereas b stands to one of the six color permutations. The reader is referred to Stefanutti et al, ( 2021 ) for the complete list of problem states codings.…”

“…A Markov model of the solution process of a problem-solving task was proposed in Stefanutti et al, ( 2021 ). The model provides a stochastic framework for the deterministic models described in Section “ Procedural knowledge space theory ”.…”

“…The model provides a stochastic framework for the deterministic models described in Section “ Procedural knowledge space theory ”. It has been empirically validated for the case of the ToL test (Stefanutti et al, 2021 ), where it obtained a satisfactory goodness-of-fit.…”

“…In PKST, the problem space formally represents how a family of problems can be solved and the knowledge space represents the skills required for solving those problems. The Markov solution process model (MSPM) by Stefanutti et al ( Journal of Mathematical Psychology, 103 , 102552, 2021 ) provides a probabilistic framework for modeling the solution process of a task, via PKST. In this article, three adaptive procedures for the assessment of problem-solving skills are proposed that are based on the MSPM.…”